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No. The CAPM is an equilibrium model. It describes relationships between expectations. With OLS you typically estimate a distribution for realized returns in the future (or sometimes even only in the past...). $R^i_{t+1} - R^f = \delta (R^{MVE}_{t+1}-R^f) + \varepsilon_{t+1}$ is not an equation from the CAPM. The CAPM SML is: $r+E(r_i - r) = r+\beta_i ...


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The factor models are based on the following linear regression model: $(R_t - R_f)$ = $\alpha$ + $\beta_{mkt}$*$(R_{mkt} - R_f)$ + $\sum\limits_{i=1}^n {x_{k,t}}$ + $\epsilon_t$ $\alpha$ is the regression model intercept and indicates the portfolio performance in excess to the market excess return and the other factor; It has to be strictly positive and ...


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(1) To get an arbitrage, buy low and sell high. Consider the following strategy: at $k$, in the event $V_k(\Phi_1) < V_k(\Phi_2)$, buy $\Phi_1$ and sell $\Phi_2$ invest the difference at the risk free rate. At maturity, your portfolio is worth what the you put in the bank plus interest. Formally, if $V_t(\Phi_\alpha) = \sum_{i=0}^d \Phi^i_{\alpha,t} ...


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Regarding (1). Assume for some time $k$, $\mathcal{V}_k(\Phi_1) > \mathcal{V}_k(\Phi_2)$ (w.l.o.g.) with full knowledge that these strategies have equal value at $T$ ,($\mathcal{V}_T(\Phi_1)=\mathcal{V}_T(\Phi_2)$). I claim that this situation admits arbitrage. I can sell $\mathcal{V}_k(\Phi_1)$ and buy $\mathcal{V}_k(\Phi_2)$ and pocket the ...


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Unfortunately, I do not know the model you talk about. However, the law of one price is a direct implication of the no-arbitrage assumption, which is assumed in many models (if not all). I do agree that the law of one price should be stated as a theorem rather than a definition. Anyway. Consider the case in which two portfolios A and B have the same value ...



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